A Family of Theta-Function Identities Based upon Combinatorial Partition Identities Related to Jacobi’s Triple-Product Identity
Date
2020
Authors
Srivastava, H.M.
Srivastava, Rekha
Chaudhary, Mahendra Pal
Uddin, Salah
Journal Title
Journal ISSN
Volume Title
Publisher
Mathematics
Abstract
The authors establish a set of six new theta-function identities involving multivariable R-functions which are based upon a number of q-product identities and Jacobi’s celebrated triple-product identity. These theta-function identities depict the inter-relationships that exist among theta-function identities and combinatorial partition-theoretic identities. Here, in this paper, we consider and relate the multivariable R-functions to several interesting q-identities such as (for example) a number of q-product identities and Jacobi’s celebrated triple-product identity. Various recent developments on the subject-matter of this article as well as some of its potential application areas are also briefly indicated. Finally, we choose to further emphasize upon some close connections with combinatorial partition-theoretic identities and present a presumably open problem.
Description
Keywords
theta-function identities, multivariable R-functions, Jacobi's triple-product identity, Ramanujan's theta functions, q-product identities, Euler's pentagonal number theorem, Rogers-Ramanujan continued fraction, Rogers-Ramanujan identities, combinatorial partition-theoretic, Schur’s, the Göllnitz-Gordon’s and the Göllnitz’s partition identities, Schur’s second partition theorem
Citation
Srivastava, H. M., Srivastava, R., Chaudhary, M. P., & Uddin, S. (2020). A family of theta-function identities based upon combinatorial partition identities related to Jacobi’s triple-product identity. Mathematics, 8(6). https://doi.org/10.3390/math8060918